Presents concluding remarks to a symposium, "The Social Organization of Knowledge and Practice." Focuses on high aptitude of persons in everyday situations to solve problems and make decisions. Addresses three questions: (1) What happens when a problem-solver reaches a situation involving calculation? (2) How does learning transfer take place? and…

Forty-six junior high students were administered six tests after a variety of instructional units using PLATO and classroom instruction. Twenty-seven procedural errors in signed-number arithmetic problems were classified into two groups to facilitate investigating error changes at different times and designing remedial instruction. (BS)

Traces history of instructional technology, including Skinner's work, Gagne's task analytic approach, and contemporary efforts associated with the cognitive revolution. It is suggested that an understanding of cognitive development improves earlier approaches by adapting them directly to students' cognitive development levels. Recent instructional…

This theoretical analysis articulates verbal rule properties and use implications, describes an empirical study examining characteristics of problem solving performance when verbal rules are instructed as a problem solving method, and discusses role of verbal rules in problem solving and implications for learning procedural skills. (MBR)

Compares performance of 172 children aged 7 to 13 years on tasks involving visual or auditory presentation of rhyming and nonrhyming letters and an oral or written response. Results indicate insensitivity to phonological similarity for young children with disabilities; sensitivity improves with age, but deficits in short-term memory remain at…

The development of proportional reasoning has long been recognised as a central but problematic aspect of mathematics learning. In a Year 6 teaching intervention the part/whole notion of fractions was distinguished from the part: part notion of ratio, and the "between" and "within" relationships in ratio were emphasised.…

This study investigated the development of an additive schema from the perspective of the schema's flexibility in coping with new context and unfamiliar semantic structure. It followed 27 first graders who learned addition and subtraction using an experimental curriculum. The instruction involved a didactical model combining the context of two…

This book contains a collection of multiplication lessons that support curriculum and instruction. The goals of the lessons are to give all students the chance to learn how to mentally multiply by 10, powers of 10, and multiples of 10; use the distributive property to calculate products; use paper and pencil to record thinking when solving…

Arithmetic is the major focus of elementary mathematics instruction. This book contains a series of lessons designed to meet the goals of place value instruction and give students a rich understanding of how the number system works. Topics include counting larger numbers in two or more ways, recognizing that the number of objects in a group…

The paper is focused on recent researches in neuroscience and developmental psychology regarding mathematical abilities of infants. A model that tries to explain these findings is developed. The model underlies the mental operations that could be systematically trained to generate efficient school learning. The model is built from a cognitive…

This guide contains classroom-tested problems designed to introduce and reinforce mathematical concepts in a quick, "fun" way. Activities emphasize the logic and reasoning skills needed to build a strong foundation in mathematics. The problems are thinking activities and require only upper elementary level mathematics skills. Activities are…

This study compared intact beginning fifth grade classes in one of the districts in Shanghai, People's Republic of China to American Norms on the KeyMath-Revised: A Diagnostic Inventory of Essential Mathematics (KeyMath-R) and the Wide Range Achievement Test (WRAT-3). The review of literature contrasted the two cultures with regard to students,…

The United States Bureau of Education in the spring of 1924 requested teachers to submit instances or illustrations of motivated work in arithmetic. The 5,000 or more replies received are doubtless a typical cross section of what is happening the country over. Replies have come from all parts of the country, especially, as was to be expected, from…

Twenty student tutors were each matched with two elementary school children, one judged to be compatible and one incompatible on the basis of a test of interpersonal relations. After nine one-hour weekly tutoring sessions (in remedial arithmetic) no significant relations were found between student achievement and either compatibility or tutor…